Searcharxiv⌕ Search

arXiv subjects

Tung-Han Hsieh

Publications and source records attributed to Tung-Han Hsieh.

At least 19 recordsLinked to original sources
arXiv2026

RG-Invariant Symmetry Ratio for QCD: A Study of $U(1)_A$ and Chiral Symmetry Restoration

We introduce a renormalization-group-invariant (RGI), scheme-independent symmetry ratio $\kappa_{AB}$, for the quantitative characterization of symmetry breaking in QCD. As a first application, we employ $\kappa_{AB}$ to investigate the relative strength of $SU(2)_L \times SU(2)_R$ chiral symmetry and $U(1)_A$ axial symmetry breaking in $N_f=2+1+1$ lattice QCD using optimal domain-wall fermions at the physical point. Our study covers three lattice spacings and twelve temperatures in the range 164--385~MeV. We examine three independent symmetry-breaking channels in the nonsinglet sector with quark-connected correlators: the $U(1)_A$-sensitive scalar--pseudoscalar channel ($\kappa_{PS}$), probing the $\pi$--$\delta$ system; the $SU(2)_L \times SU(2)_R$-sensitive vector--axial-vector channel ($\kappa_{VA}$), probing the $\rho$--$a_1$ system; and an additional $U(1)_A$-sensitive tensor vector--axial-tensor vector channel ($\kappa_{TX}$), probing the $\rho_T$--$b_1$ system. At finite lattice spacing, we observe a clear hierarchy $\kappa_{PS} > \kappa_{VA} > \kappa_{TX}$. A controlled continuum extrapolation reveals that this hierarchy collapses, with all three symmetry-breaking strengths becoming statistically indistinguishable within our precision. This result provides a new, model-independent benchmark from a chirally symmetric lattice action. Our findings indicate that in the continuum limit the $SU(2)_L \times SU(2)_R$ and $U(1)_A$ channels in the nonsinglet sector reach degeneracy at the same temperature, already at the lowest simulated point of $164$~MeV, so that the two symmetries restore concurrently near the chiral crossover rather than at parametrically separated scales.

hep-lat↗
arXiv2022

Topological susceptibility in finite temperature QCD with physical $(u/d, s, c)$ domain-wall quarks

We perform hybrid Monte-Carlo (HMC) simulation of lattice QCD with $N_f=2+1+1$ domain-wall quarks at the physical point, on the $64^3 \times (64,20,16,12,10,8,6)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this paper, we determine the topological susceptibility of the QCD vacuum for $T > T_c \sim 150 $ MeV. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility $ χ_t(a,T) $ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility $χ_t(a,T) $ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T \sim 155-516 $ MeV, we extract the topological susceptibility $χ_t(T)$ in the continuum limit. To compare our results with others, we survey the continuum extrapolated $χ_t(T)$ in lattice QCD with $N_f=2+1(+1)$ dynamical quarks at/near the physical point, and discuss their discrepancies. Moreover, a detailed discussion on the reweighting method for domain-wall fermion is presented.

hep-lat↗
arXiv2022

Finite temperature QCD with physical $(u/d, s, c)$ domain-wall quarks

In order to understand the role of QCD in the early universe, we perform hybrid Monte-Carlo simulation of lattice QCD with $N_f=2+1+1$ optimal domain-wall quarks at the physical point, on the $64^3 \times (6,8,10,12,16,20,64)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this Proceeding, we present our first result on the topological susceptibility of the QCD vacuum. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility $ χ_t(a,T) $ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility $χ_t(a,T) $ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T \sim 155-516 $~MeV, we extract the topological susceptibility $χ_t(T)$ in the continuum limit.

hep-lat↗
arXiv2019

Topological susceptibilty in lattice QCD with exact chiral symmetry -- the index of overlap-Dirac operator versus the clover topological charge in Wilson flow

Using an ensemble of 535 gauge configurations (on the $24^4 \times 48 $ lattice with $ a \simeq 0.06 $~fm and $ M_π \simeq 260 $~MeV) which are generated by hybrid Monte Carlo (HMC) simulation of $N_f=2$ lattice QCD with the optimal domain-wall quark, we compute the index of the overlap-Dirac operator, and also measure the clover topological charge in the Wilson flow, $Q_{\text{clover}}(t) $, by integrating the flow equation from $ t = 0 $ to $ t = 128 $ with $δt = 0.01 $. We observe that $Q_{\text{clover}}(t) $ of each configuration converges to a value close to an integer, and its nearest integer $Q_c(t) = \text{round} [Q_{\text{clover}}(t)] $ becomes invariant for $ t \ge t_c $, with the $ \max\{t_c \} \sim 77 $ for all 535 configurations. For each configuration, we compare the asymptotically-invariant $ Q_c $ with the index of overlap-Dirac operator at $t=0$. It turns out that there are 167 configurations with $Q_c \ne \text{index}(D_{o}) $, amounting to $31.2\%$ of the total 535 configurations. However, the histograms of $ Q_c $ and $ \text{index}(D_o) $ are almost identical. Consequently, the topological susceptibility using the asymptotically-invariant $ Q_c $ agrees with that using the index of overlap-Dirac operator at $ t=0 $. This implies that the topological susceptibility in lattice QCD with exact chiral symmetry can be obtained from the asymptotically-invariant $ Q_c $ in the Wilson flow.

hep-lat↗
arXiv2014

Decay Constants of Pseudoscalar $D$-mesons in Lattice QCD with Domain-Wall Fermion

We present the first study of the masses and decay constants of the pseudoscalar $ D $ mesons in two flavors lattice QCD with domain-wall fermion. The gauge ensembles are generated on the $24^3 \times 48 $ lattice with the extent $ N_s = 16 $ in the fifth dimension, and the plaquette gauge action at $ β= 6.10 $, for three sea-quark masses with corresponding pion masses in the range $260-475$ MeV. We compute the point-to-point quark propagators, and measure the time-correlation functions of the pseudoscalar and vector mesons. The inverse lattice spacing is determined by the Wilson flow, while the strange and the charm quark masses by the masses of the vector mesons $ ϕ(1020) $ and $ J/ψ(3097) $ respectively. Using heavy meson chiral perturbation theory (HMChPT) to extrapolate to the physical pion mass, we obtain $ f_D = 202.3(2.2)(2.6) $ MeV and $ f_{D_s} = 258.7(1.1)(2.9) $ MeV.

hep-lat↗
arXiv2013

Chiral symmetry and axial U(1) symmetry in finite temperature QCD with domain-wall fermion

We study the restoration of the spontaneously broken chiral symmetry and the anomalously broken axial U(1) symmetry in finite temperature QCD at zero chemical potential. We use 2 flavors lattice QCD with optimal domain-wall fermion on the $ 16^3 \times 6 $ lattice, with the extent $ N_s = 16 $ in the fifth dimension, in the temperature range $ T = 130-230 $ MeV. To examine the restoration of the chiral symmetry and the axial $ U(1) $ symmetry, we use diluted $ Z_2 $ noises to calculate the chiral condensate, and the chiral susceptibilities in the scalar and pseudoscalar meson channels, for flavor singlet and non-singlet respectively. From the degeneracy of the chiral susceptibilities around $ T_c $, it suggests that the axial $ U(1) $ symmetry is restored in the chirally symmetric phase. Moreover, we examine the spectral density $ ρ(λ_c) $ of the 4D effective Dirac operator with exact chiral symmetry, which is obtained by computing zero modes plus (180+180) conjugate pairs of low-lying modes for each gauge configuration. The suppression of low modes in the spectral density provides a consistency check of the restoration of axial $ U(1) $ symmetry in the chirally symmetric phase.

hep-lat↗
arXiv2012

Pseudoscalar Meson in Two Flavors QCD with the Optimal Domain-Wall Fermion

We perform hybrid Monte Carlo (HMC) simulatons of two flavors QCD with the optimal domain-wall fermion (ODWF) on the 16^3 x 32 lattice (with lattice spacing a ~ 0.1 fm), for eight sea-quark masses corresponding to pion masses in the range 228-565 MeV. We calculate the mass and the decay constant of the pseudoscalar meson, and compare our data with the chiral perturbation theory (ChPT). We find that our data is in good agreement with the sea-quark mass dependence predicted by the next-to-leading order (NLO) ChPT, and provides a determination of the low-energy constants \bar{l}_3 and \bar{l}_4, the pion decay constant, the chiral condensate, and the average up and down quark mass.

hep-lat↗
arXiv2011

Topological Susceptibility in Two Flavors Lattice QCD with the Optimal Domain-Wall Fermion

We determine the topological susceptibility of the gauge configurations generated by lattice simulations using two flavors of optimal domain-wall fermion on the $ 16^3 \times 32 $ lattice with length 16 in the fifth dimension, at the lattice spacing $ a \simeq 0.1 $ fm. Using the adaptive thick-restart Lanczos algorithm, we project the low-lying eigenmodes of the overlap Dirac operator, and obtain the topological charge of each configuration, for eight ensembles with pion masses in the range $ 220-550 $ MeV. From the topological charge, we compute the topological susceptibility and the second normalized cumulant. Our result of the topological susceptibility agrees with the sea-quark mass dependence predicted by the chiral perturbation theory and provides a determination of the chiral condensate, $Σ^{\bar{MS}}(2 GeV)=[259(6)(7) MeV]^3 $, and the pion decay constant $F_π= 92(12)(2)$ MeV.

hep-lat↗
arXiv2011

Topological Charge in Two Flavors QCD with Optimal Domain-Wall Fermion

We measure the topological charge of the gauge configurations generated by lattice simulations of 2 flavors QCD on a $ 16^3 \times 32 $ lattice, with Optimal Domain-Wall Fermion (ODWF) at $ N_s = 16 $ and plaquette gauge action at $ β= 5.90 $. Using the Adaptive Thick-Restart Lanczos algorithm, we project the low-lying modes of the 4D effective Dirac operator of ODWF, and obtain the topological charge and topological susceptibility. Our result of topological susceptibility agrees with the sea-quark mass dependence predicted by the chiral perturbation theory, and provides a determination of the chiral condensate.

hep-lat↗
arXiv2011

Lattice QCD with Optimal Domain-Wall Fermion: Light Meson Spectroscopy

We perform lattice simulations of two flavors QCD using the optimal domain-wall fermion, in which the chiral symmetry is preserved to a good precision ($ m_{res} \sim 0.3 $ MeV) on the $ 16^3 \times 32 $ lattice ($ L \sim 2 $ fm) with inverse lattice spacing $ a^{-1} \sim 1.8 $ GeV, and $ N_s = 16 $ in the fifth dimension, for eight sea quark masses corresponding to the pion masses in the range 210-500 MeV. We present our first results of the mass and the decay constant of the pseudoscalar meson, which are in good agreement with the next-to-leading order chiral perturbation theory for $ M_π< 450 $ MeV, and from which we determine the low-energy constants $ f $, $ Σ$, $ \bar{l}_3 $ and $ \bar{l}_4 $. At the physical pion mass $ M_π = 135$ MeV, we obtain the pion decay constant $f_π=133(1)(2)$ MeV, and the average up and down quark mass $m_{ud}^{\bar{\rm MS}}(\mathrm{2 GeV})=4.09(7)(11)$ MeV, where the first error is statistical, and the second error is systematic due to the truncation of the higher order corrections and the uncertainty in the determination of the lattice spacing. Furthermore, we also obtain the chiral condensate $ Σ^{\bar{\mathrm{MS}}}(2 GeV) = [250(4)(7) MeV]^3 $.

hep-lat↗
arXiv2011

GPU-Based Conjugate Gradient Solver for Lattice QCD with Domain-Wall Fermions

We present the first GPU-based conjugate gradient (CG) solver for lattice QCD with domain-wall fermions (DWF). It is well-known that CG is the most time-consuming part in the Hybrid Monte Carlo simulation of unquenched lattice QCD, which becomes even more computational demanding for lattice QCD with exact chiral symmetry. We have designed a CG solver for the general 5-dimensional DWF operator on NVIDIA CUDA architecture with mixed-precision, using the defect correction as well as the reliable updates algorithms. We optimize our computation by even-odd preconditioning in the 4D space-time lattice, plus several innovative techniques for CUDA kernels. For NVIDIA GeForce GTX 285/480, our CG solver attains 180/233 Gflops (sustained).

hep-lat↗
arXiv2009

TWQCD's dynamical DWF project

We present an overview of our project of simulation of unquenched lattice QCD with optimal domain-wall quarks, using a GPU cluster currently constituting of 16 units of Nvidia Tesla S1070 plus 64 graphic cards with Nvidia GTX285 (total 128 GPUs with 128 Teraflops peak), attaining sustained computing power of 15.36 Teraflops. The first production run in two-flavor QCD is on-going, using the Iwasaki gauge action on a set of lattices with sizes $ 16^3 \times (32,10,8,6,4) \times (16,32) $ at the lattice spacing $ a \sim 0.1$ fm, with eight sea quark masses down to $ m_π\simeq 200 $ MeV. We outline our simulation algorithm, and describe the present status of the production run. Preliminary results of pseudoscalar mass and decay constant are also presented.

hep-lat↗
arXiv2009

One-flavor algorithm for Wilson and domain-wall fermions

We construct positive-definite pseudofermion actions for one fermion flavor in lattice field theory, for Wilson and domain-wall fermions respectively. The positive definiteness of these actions ensures that they can be simulated with the Hybrid Monte Carlo (HMC) method. For lattice QCD with optimal domain-wall quarks, we compare the efficiency of HMC simulations of 2-flavor and (1+1)-flavor, and find that the efficiency ratio is about 3:2.

hep-lat↗
arXiv2008

Topological susceptibility in 2+1 flavors lattice QCD with domain-wall fermions

We measure the topological charge and its fluctuation for the gauge configurations generated by the RBC and UKQCD Collaborations using 2+1 flavors of domain-wall fermions on the 16^3 x 32 lattice (L \simeq 2 fm) with length 16 in the fifth dimension at inverse lattice spacing a^{-1} \simeq 1.62 GeV. From the spectral flow of the Hermitian operator H_w (2 + γ_5 H_w)^{-1}, we obtain the topological charge Q_t of each gauge configuration in the three ensembles with light sea quark masses m_q a = 0.01, 0.02, and 0.03, and with the strange quark mass fixed at m_s a = 0.04. From our result of Q_t, we compute the topological susceptibilty χ_t = < Q_t^2 > /volume. In the small m_q regime, our result of χ_t agrees with the chiral effective theory. Using the formula χ_t = Σ/ (m_u^{-1} + m_d^{-1} + m_s^{-1}) by Leutwyler-Smilga, we obtain the chiral condensate Σ^MSbar(2 GeV) = [259(6)(9) MeV]^3.

hep-lat↗
arXiv2007

Dirac b quark on the lattice

We perform the first study of treating b, c, and s quarks as Dirac fermions in lattice QCD with exact chiral symmetry. On a 32^3 60 lattice with 1/a ~ 7.68 GeV, we compute point-to-point quark propagators, and measure the time-correlation functions for mesons with quark contents b_bbar, c_bbar, s_bbar, and c_cbar. The lowest-lying meson mass spectra, the pseudoscalar decay constants, and the b and c quark masses are determined.

hep-lat↗
arXiv2007

Beauty mesons in lattice QCD with exact chiral symmetry

We present the first study of treating b, c, and s quarks as Dirac fermions in lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at beta = 7.2 on the 32^3 x 60 lattice, we compute point-to-point quark propagators for 33 quark masses in the range 0.01 < m_q a < 0.85, and measure the time-correlation function of (pseudo-)scalar, (pseudo-)vector, and tensor mesons, for symmetric and asymmetric quark masses respectively. The lowest-lying mass spectra of mesons with quark contents b_bbar, c_bbar, s_bbar, and c_cbar are determined, together with the pseudoscalar decay constants. Our results are sumarized in Tables 1-5. Furthermore, we also determine the b and c quark masses in the MS_bar scheme, m_b = 4.65(5) GeV, and m_c = 1.16(4) GeV.

hep-lat↗
arXiv2007

Bs and Bc mesons in lattice QCD with exact chiral symmetry

We determine the masses and decay constants of the pseudoscalar mesons Bs and Bc, and also the masses of the vector mesons Bs^* and Bc^*, in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at beta = 7.2 on the 32^3 x 60 lattice, we compute point-to-point quark propagators for 33 quark masses in the range [0.01, 0.85], and measure the time-correlation functions of pseudoscalar and vector mesons. The inverse lattice spacing and the charm quark bare mass are determined using the mass and decay constant of eta_c(2980). The bare masses of s and b quarks are chosen such that the masses of the corresponding vector mesons are in good agreement with phi(1020), and Upsilon(9460) respectively. Our results are: m_{Bs} = 5385(27)(17) MeV, f_{Bs} = 253(8)(7) MeV, m_{Bc} = 6278(6)(4) MeV, f_{Bc} = 489(4)(3) MeV, m_{Bs^*} = 5424(28)(19) MeV, and m_{Bc^*} = 6315(6)(5) MeV.

hep-lat↗